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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Remark on Walter's inequality for Schur multipliers


Author: Marek Bożejko
Journal: Proc. Amer. Math. Soc. 107 (1989), 133-136
MSC: Primary 47B38; Secondary 42B15
MathSciNet review: 1007285
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Abstract: We extend and give another proof of Walter's inequality: For a linear operator $ T \in L({l^2}(X))$

$\displaystyle \vert\vert T\vert\vert _{{V_2}(X)}^2 \leq \vert\vert\,\vert T{\ve... ...}\vert{\vert _{{V_2}(X)}}\vert\vert\,\vert T{\vert _r}\vert{\vert _{{V_2}(X)}},$

where $ {V_2}(X)$ is the Banach algebra of Schur multipliers on $ L({l^2}(X))$ and $ \vert T{\vert _l} = {(TT)^{*1/2}},\vert T{\vert _r} = \vert{T^*}{\vert _l}$.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-1007285-7
PII: S 0002-9939(1989)1007285-7
Keywords: Schur multipliers, Schur product
Article copyright: © Copyright 1989 American Mathematical Society